(2b+5)(b-1)=6b

Solution for (2b+5)(b-1)=6b equation:

(2b+5)(b-1)=6b

We move all terms to the left:

(2b+5)(b-1)-(6b)=0

We add all the numbers together, and all the variables

-6b+(2b+5)(b-1)=0

We multiply parentheses ..

(+2b^2-2b+5b-5)-6b=0

We get rid of parentheses

2b^2-2b+5b-6b-5=0

We add all the numbers together, and all the variables

2b^2-3b-5=0

a = 2; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·2·(-5)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*2}=\frac{-4}{4}
=-1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*2}=\frac{10}{4}
=2+1/2
$